Development and testing of a subgrid-scale model for moving-boundary hydrodynamic problems in shallow water

Over the past 20 years numerical algorithm advances and increased computing power have led to the development of high-resolution hydrodynamic models f or a variety of shallow-water flow problems. Despite the success of these a pproaches a number of fundamental constraints remain, in particular the sim ulation of flows that involve rapid changes in the position of the fluid bo undary, for example river and coastal floods, tidal flows and dam breaks, i s still extremely difficult. Given the relative difficulty of developing de formable meshing techniques that adapt to the flow evolution, most hydrauli c models utilize a fixed-grid approach and use a correction algorithm for f low over partially wet elements. A range of techniques are available from s imple grid-cell exclusion/inclusion methods to reformulation of the control ling hydrodynamic equations based on a knowledge of the subgrid topography. Although the latter approach retains the most realism, a number of problem s with its implementation remain unresolved. These include the lack of a tr ansparent sequence of numerical development and the need for a scheme that incorporates both mass and momentum corrections for partially wet elements. Moreover, in testing the scheme there is a clear requirement for a rigorou s and objective test for such problems to be defined. In this paper a new s ubgrid-scale approach to dynamic wetting and drying in shallow water is the refore developed that overcomes these constraints. In particular a test cas e consisting of a sinusoidal tide on a planar beach is developed where wate r depths across the domain at each time-step are known independently of the model and compared with simulations conducted using both standard finite-e lement methods and the new technique. This comparison demonstrates that the new model gives a significant improvement in predicted hydraulics, particu larly on the wetting phase. Moreover, it is shown that the new scheme appli ed to a low-resolution mesh outperforms standard methods solved using much higher resolution grids. The possibility is also raised that standard metho ds will always fail to capture wetting and drying processes adequately. Thi s is critical as the simulations conducted show that the accurate capture o f such hydrodynamic effects near the boundary has a significant impact on p redictions over the entire domain. Copyright (C) 2000 John Wiley & Sons, Lt d.